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Econ206

# Econ206 - Economics 206 Spring 2007(Prof G Loury Answers...

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Economics 206 Spring 2007 (Prof. G. Loury) Answers for Assignment 9: The Principal-Agent Problem (1) This is a simple example of the Principal-Agent problem where the agent’s (unob- servable) e f ort level can be any non-negative number, but only two (observable) levels of performance for the project are possible. If the project succeeds its gross value is V> 0 . If the project fails, its value is 0 . The probability of success, p ( e ) , depends on the agent’s e f ort, e 0 . In this setting a contract ( w 0 ,w 1 )speci f es what the agent receives conditional on project success ( w 1 ) or failure ( w 0 ). The agent’s utility function is quasi-linear: u ( w,e )= v ( w ) e, v 0 ( w ) > 0 ,v 00 ( w ) 0 . The agent will only accept a contract if it generates expected utility u u 0 . a. The f rst task is to f nd the optimal contract when the agent is risk-neutral and when the wage can be negative. The essence of the principal-agent contract design problem lies in the trade-o f between providing e f ort incentives to the agent and allocating risk-bearing e ciently between the two parties. We know from discussion in the text and in the lectures that when the agent is risk neutral the principal extracts maximum surplus out of the project by, in e f ect, transfering ownership of the project to the agent for a f xed fee, which gives the agent the proper e f ort incentives while causing him to bear all of the risk. This risk bearing is costless when the agent is risk neutral. In the case of risk neutrality, I assume without loss of generality that v ( w )= w .L e t K denote the maximal net surplus from the project. This may be expressed as follows: K Max e 0 { p ( e ) V e } u 0 . (We need to assume u 0 is not too big, so that K > 0 .) Given our assumptions, the solution for this maximization problem is attained at e = e ,suchthat : p 0 ( e )= 1

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Econ206 - Economics 206 Spring 2007(Prof G Loury Answers...

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